Trends in the Transitory Variance of Male Earnings in the U.S., 1991-2003: Preliminary Evidence from LEHD data1 Peter Gottschalk Boston College Erika McEntarfer U.S. Department of the Treasury Robert Moffitt Johns Hopkins University December, 2008 Prepared for presentation at the meetings of the American Economic Association, San Francisco, January 2009. The authors would like to thank Shannon Phillips and Anna Blank for outstanding research assistance. 1 This document reports the results of research and analysis undertaken by the U.S. Census Bureau staff. It has undergone a Census Bureau review more limited in scope than that given to official Census Bureau publications. This document is released to inform interested parties of ongoing research and to encourage discussion of work in progress. This research is a part of the U.S. Census Bureau’s Longitudinal Employer-Household Dynamics Program (LEHD), which is partially supported by the National Science Foundation Grants SES-9978093 and SES-0427889 to Cornell University (Cornell Institute for Social and Economic Research), the National Institute on Aging Grant R01~AG018854, and the Alfred P. Sloan Foundation. The views expressed herein are attributable only to the author(s) and do not represent the views of the U.S. Census Bureau, its program sponsors or

data providers, or of the Board of Governors of the Federal Reserve System or its staff. Some or all of the data used in this paper are confidential data from the LEHD Program. The U.S. Census Bureau supports external researchers’ use of these data through the Research Data Centers (see www.ces.census.gov). For other questions regarding the data, please contact Jeremy S. Wu, Manager, U.S. Census Bureau, LEHD Program, 4700 Silver Hill Rd., Suitland, MD 20233, and USA. (Jeremy.S.Wu@census.gov)

Abstract

Trends in the Transitory Variance of Male Earnings

in the U.S., 1991-2003: Preliminary Evidence from the LEHD

We estimate the trend in the transitory variance of male earnings in the U.S. from 1991 to

2005 using an administrative data set of Unemployment Insurance wage reports, the

Longitudinal Employer-Employer Dynamics data set (LEHD), and compare the findings to those

of Moffitt and Gottschalk (2008) obtained from the Michigan Panel Study of Income Dynamics

(PSID). Despite substantial differences between the LEHD and the PSID in the levels of cross-

sectional variances of male earnings, the changes over time in transitory variances obtained from

estimating two of the models in Moffitt and Gottschalk are quite similar in the two data sets.

Specifically, over the 1991-2003 period, transitory variances fell slightly, and then rose slightly,

returning in 2003 to the same approximate level they had obtained in 1991. Overall, the analysis

of the LEHD data confirms the findings based on the PSID that the transitory variance did not

show a trend net of cycle over this period.

A substantial literature has developed on estimates of various measures of trends in

earnings and income instability in the U.S. and some other countries. Virtually all of the U.S.

studies have employed the Michigan Panel Study of Income Dynamics (PSID), a longitudinal

household survey of families begun in 1968 (Gottschalk and Moffitt, 1994; Moffitt and

Gottschalk, 1995, 2008; Dynarski and Gruber, 1997; Cameron and Tracy, 1998; Haider, 2001;

Hyslop, 2001; Moffitt and Gottschalk, 2002; Dynan et al., 2008; Jensen and Shore, 2008; Shin

and Solon, 2008).1 Those studies which focus on computing the classical transitory variance of

earnings have virtually all shown increases for men, although many have found increases that

were concentrated primarily in the 1980s. For example, the recent study of Moffitt and

Gottschalk (2008) found that the transitory variance of male earnings stopped growing sometime

in the late 1980s or early 1990s, and exhibited no further trend through 2004.

A concern with all studies using the PSID is measurement error, mostly arising from

errors in reported earnings2. The PSID has traditional earnings questions which ask respondents

to report earnings over the previous calendar year and, as noted in the review paper by Bound et

1 One study (Dahl et al., 2008) used an administrative data set, the Continuous Wage

Benefit History data which have reports of Social Security earnings. They found results in contrast to the PSID but the difference may have been a result of a difference in the measure of instability used. See Moffitt and Gottschalk (2008) for a discussion.

2 Errors may also arise from imputation procedures used by the survey organization to deal with missing answers (don’t knows and refusals) and seemingly extreme value answers (outliers). The effect of these sources of error can be dealt with by excluding imputed earnings, though this raises potential selection issues, and by trimming the data.

al. (2001), measurement error is known to occur in this case, including the PSID. Moreover,

measurement error is known to be non-classical, both correlated with observable characteristics,

serially correlated (usually mean reverting).. However, the magnitude of the resulting impacts on

estimates of the covariance structure of earnings equations may not be large (Pischke, 1995;

Brown et al., 2001). Gottschalk and Huynh (forthcoming) show that this is a result of large but

offsetting effects of the non-classical attributes of measurement error in both earnings and lagged

earnings.

A consideration relevant to our goal of estimating trends in the transitory variance of

earnings is that measurement error may affect only our estimated levels of that variance and not

its trend, if the character of measurement error has not changed over time. Unfortunately, the

PSID made several changes to its procedures in the early 1990s, when it shifted from “paper and

pencil” telephone interviewing to computer-assisted telephone interviewing in 1993, which could

be expected to affect measurement error (Kim et al., 2000). Around the same time, the PSID

changed its method of imputation for missing or outlying earnings values, moving from using a

set of discretionary rules for individual items to a more conventional hot-deckprocedure. The

early 1990s is an important period for trends in earnings dynamics, for it is in that period that

Moffitt and Gottschalk (2008) determine that the upward trend in the transitory variance stopped

growing, with some ambiguity as to the exact date because of a recession that occurred in the US

at that time. While one could argue that the fact that the transitory variance exhibited no further

trend from the early 1990s to 2005 is valid if PSID procedures remaining unchanged over that

time, the PSID change in procedures does affect a comparison of that period with earlier

periods.3

In this paper, we estimate U.S. permanent and transitory variances with an

administrative-record data set, the Longitudinal Employer-Household Dynamics (LEHD) data

set, which is based upon the universe of all employer reports of quarterly earnings for the

Unemployment Insurance system. Such reports are generally thought to be less contaminated

by measurement error than survey reports, so the variance estimates on such data should be

indirectly informative of the impact of measurement error on PSID-based estimates. The LEHD

data are only available since 1991, however, and they have some other non-comparabilities with

the PSID and other issues, which we discuss below.

We first inspect the raw LEHD data and find that it shows marked differences in cross-

sectional means and variances of log earnings compared to the Current Population Survey (CPS)

and the PSID, differences that are difficult to explain. However, we also find that trends in the

raw mean and variance of log earnings closely mirror those in the PSID and the CPS. We then

apply two of the methods for the estimation of transitory variances developed by Moffitt and

Gottschalk (2008) to the LEHD data. Our results show that, while the levels of transitory

variances estimated are again different from those estimated with PSID data, the trends are quite

similar in the two data sets for the 1991-2003 overlap period.

In the remainder of this research note, we first describe the LEHD data and compare it to

the PSID. We then briefly summarize the estimation procedures developed by Moffitt and

Gottschalk (2008), describe how we apply them to the LEHD data, and report our results. A

3 Gouskova and Schoeni (2007) compared cross-sectional estimates of the distribution of

PSID and CPS income reports over this period and argue that the two exhibit the same trends and

short summary concludes.

The Longitudinal Employer-Household Dynamics Data Set

As described in more detail in Abowd et al. (2004, 2006), the Longitudinal Employer-

Household Dynamics program is a program at the U.S. Bureau of the Census that encompasses

several different administrative and linked administrative-survey data sets. Here, we use the

LEHD data set consisting of the wage data available from state-level unemployment insurance

(UI) programs, originating from employer reports to state agencies for purposes of determining

entitlement to UI benefits. These data contain uncapped quarterly earnings for employees

covered by state unemployment insurance systems, estimated to cover over 95 percent of private

sector employment. Although coverage laws vary slightly from state to state, state, UI programs

generally do not cover federal employees, most agricultural workers, many churches and non-

profits, and the self-employed.4 These administrative earnings records can be linked across

quarters to create individual work histories. The gender and date of birth of individuals are

available from links to the Census NUMIDENT file (a version of the Social Security

Administration transaction file)

The LEHD program is of fairly recent origin, but agreements between the U.S. Census

Bureau have been negotiated for 44 states as of this writing. However, most state data do not

extend far back in time. For this reason, we select only five large states for our analysis, those

that, therefore, the PSID procedural changes had no effects on the trends.

4 The LEHD program is currently integrating administrative data sources on the self-employed and federal workers, however those data were not yet available at the time of this analysis.

whose data are available back to 19915. The most recent data are from 2003. We restrict our

sample to male workers age 23-62 in any year in the sample, for comparability with the work of

Moffitt and Gottschalk (see below). We also exclude those who have only one quarter of LEHD

earnings . These include seasonal workers with very low earnings whose earnings are unlikely to

be reported in the PSID and whose inclusion in the LEHD has a large impact on the variance of

log earnings (further work on this is underway). For some analyses, we additionally trim the

top and bottom 1 percent of the earnings distribution, as described below (again, for

comparability with Moffitt and Gottschalk,2008). None of the selected states have large

metropolitan areas at the border of the state that would be conducive to a large number of cross-

state transitions (and thus workers appearing and disappearing as they moved in and out of the

state UI employment universe). The final sample is quite large, with between four and six

million workers in any given year

There are some differences between this sample and the PSID sample used by Moffitt

and Gottschalk. The most important difference is likely to be the exclusion of non-household-

heads in the PSID, whose earnings are not consistently measured in that data set. The LEHD, on

the other hand, contains all workers regardless of headship status. The LEHD does not have an

indicator for headship status, so these workers cannot be identified. On a priori grounds, one

might suspect that secondary workers in a household would have more variable earnings

trajectories than those of heads. In addition to this, of course, the PSID includes the nation as a

whole, and not just five states; the PSID sample sizes are too small for any substantial analyses

on this subset of states. A minor difference is that the age range used by Moffitt and Gottschalk

5 The states are Oregon, North Carolina, Washington, Illinois, and Wisconsin.

was 20-59, but excluding individuals identified as students; student status is not available in the

LEHD, so the age range is shifted upwards by three years, to 23-62, to eliminate students in the

20-22 range.6 Moffitt and Gottschalk did not exclude workers with only one quarter of earnings,

but a sensitivity analysis to this is underway. Finally, Moffitt and Gottschalk analyzed residuals

from a first-stage log earnings regression with independent variables for age, year, education,

and race; the LEHD analyses reported here uses raw log earnings However, Moffitt and

Gottschalk found small differences in their estimates of permanent and transitory variances of

residual or raw PSID log earnings. While we do not believe that the use of raw earnings rather

than residual earnings from the LEHD should cause differences in trends, this may explain

lower variances in the PSID analysis7.

Figures 1-3 show comparisons of the LEHD data to the CPS, the most widely used data

set for studies of earnings inequality. This comparison allows us to determine whether the

LEHD shows similar levels and trends in cross-sectional means and variances of log earnings.

One major advantage of comparing the LEHD to the CPS, rather than the PSID, is that similar

sample deletions (e.g., for the five states) can be imposed on these two data sets, thus minimizing

the effects of sample composition.8 For the CPS, we show figures for the nation as a whole and

for the five states that appear in our LEHD sample. Sample sizes are necessarily smaller in the

latter case. The CPS tabulations are for men 23-62, and are based on household reports of

6 Moffitt and Gottschalk actually restricted their sample to those 30-59, but used lags of

earnings for these individuals back to age 20. An analysis of sensitivity to this difference is also underway.

7 We are in the process of redoing the analysis for both data sets using residuals from first stage regressions that condition only on age and year.

8 The major remaining difference is that we cannot exclude workers with only one quarter

earnings in the last year taken from the March survey.9 Both data sets are trimmed at the top and

bottom 1 percent prior to tabulation .

Figure 1 shows that the LEHD log earnings means are considerably lower than those in

the CPS. 10However, the trends are roughly similar after 1996, with both means rising from

1996 through 2000 and declining after 2001, a recession year. The CPS shows a modest rise in

earnings from 1992-1993 through 1996 while the LEHD is flatter over that period.

Figure 2 shows the variance of log male earnings in these two data sets. The variance is

somewhat higher in the LEHD than in the CPS, which is consistent with the finding in

Gottschalk and Huynh (forthcoming) that measurement error in earnings is non-classical, with

higher earnings individuals underreporting their true values and lower earnings individuals over

reporting them. This leads to an attenuation in the cross-sectional variance in survey data. While

the levels are somewhat lower in the CPS than the LEHD, both data sets show relatively little

increases in the variance, though both show a mild increase starting in 1999.

While the PSID covers a substantially different subpopulation, namely male heads, it is

useful to contrast the mild increase in inequality in the 1990s found in the LEHD and CPS with

the much larger increase over the period covered by the PSID. Figure 2b shows the variance of

log earnings from 1970 to 2004 for the PSID and a CPS sample with sample cuts used to

replicate the PSID. To facilitate comparisons with the LEHD and its CPS benchmark, we also

replicate the two series shown in Figure 2a. While the PSID shows substantially lower variances

of earnings from the CPS.

9 While Federal workers are excluded from the LEHD, it is not possible to exclude these workers from the CPS since they are aggregated along with state and local workers into a single category.

than either the LEHD or the CPS benchmark of the PSID, all data sets show relatively little

increases in the log variance during the 1990s compared to the early 1980s. This is consistent

with this many other studies. There is, however, some difference in the timing of the recent mild

increase in the log variance across data sets. The PSID shows a mild increase starting in 1996

while the LEHD and the CPS benchmark of the PSID both show increases in the log variance

starting in 1998. The LEHD, however, moves less in both the downward and upward direction

in terms of magnitude, than either the PSID or CPS.

To explore whether the LEHD and CPS variances reflect similar underlying trends in

percentiles, Figures 3a and 3b show the 10th and 90th percentiles for the LEHD and its CPS

benchmark. The LEHD shows no change in the P10 from 1990 to 1996, while the CPS declines

through 1993 and then increases. The two series, however, show similar movements during the

remaining period, 1996-2006. Both increase through 1998 and then decline.11 Figures 3b also

shows roughly similar patterns in the LEHD and CPS at the 90th percentile over the full period,

with both increasing by roughly 20 percent from 1990 to 2004.

We conclude that while there are some differences in the time series patterns of

variances in the LEHD, CPS, and PSID, all three data sets show relatively flat profiles. The

changes in all three data sets after 1991 are small compared to large increases in the log variance

during the 1980s shown in our CPS and PSID samples, as well as found in many other studies,

such as Card and Dinardo (2002).

10 All dollar figures in this paper are deflated with the 1996 CPI-U-RS. 11 The CPS for all states, however, does not fall. This indicates that the very bottom of

Estimating Transitory Variances

Moffitt and Gottschalk (2008) estimated the trend in the variance of log annual earnings

of men in the PSID using the autocovariance matrix of earnings indexed by age, year, and lag

length. A typical element of this matrix consists of the covariance between earnings of men at

ages a and a’ between years t and t’. For sample size reasons, Moffitt and Gottschalk grouped

the observations into three age groups--30-39, 40-49, and 50-59--and then constructed the

variances for each age group in each year, as well as the autocovariances for each group at all

possible lags (back to 1970 or age 20, whichever came first). The covariance between the

earnings of the group in the given year and each lagged year was computed using the individuals

who were in common in the two years. The top and bottom one percent of the residuals within

age-education-year cells was trimmed to eliminate outliers and top-coded observations. The

resulting autocovariance matrix represented every individual variance and covariance between

every pair of years only once, and stratified by age so that life cycle changes in the variances of

permanent and transitory earnings can be estimated. The resulting autocovariance matrix had

1,197 elements over all ages and all years, 1971-2004.

We follow these procedures exactly for the formation of the LEHD covariance matrix

except that the four age groups are slightly older to minimize the impact of not being able to

exclude students from the LEHD: 23-32, 33-42, 43-52, and 53-62. We apply the same

trimming procedures. Because the LEHD only permits lags back to 1991 for each ten-year age

group, the resulting covariance matrix only has 283 elements.

Moffitt and Gottschalk used three methods to estimate trends in transitory variances: a

the distribution is somewhat different in the five states sampled by the LEHD.

structural error components model, an approximate nonparametric model, and a grouped model

they called the “BPEA” method. We do not apply the third-method to the LEHD data because it

requires the construction of nine-year windows of the data, and the LEHD time period (1991-

2005) is too short to allow meaningful trend inference. However, we apply the first two methods

exactly as described in Moffitt-Gottschalk (2008). We will not exposit those models here, but

refer the reader to their 2008 paper.12

Figures 4-8 show the findings from the PSID reported by Moffitt and Gottschalk. Figure

4 shows that the year factor loading on the standard deviation of the permanent component

(alpha) estimated from their parametric error components model fluctuated with no discernible

trend from 1991 to 1996 but then rose sharply through 2004. The year factor loading on the

transitory component (beta), our main object of interest, is shown in Figure 5. That variance

declined from 1991 through approximately 1998 and then rose through 2002, falling again in

2004. Moffitt and Gottschalk interpreted this as evidence for no trend after 1991. Their

interpretation is reinforced by Figure 6, which shows the unemployment rate as well. The

pattern in the transitory variance is closely aligned with the unemployment rate after about 1990,

implying that the fluctuations in the transitory variances were likely only cyclical.

Figure 7 shows the permanent, transitory, and total variances of log male earnings

12 While the error components model fitted to the LEHD data is identical to that fitted to

the PSID data, it deserves reemphasis that the LEHD have lags no more than 12 years (2003 back to 1991), whereas the PSID data have lags of up to 31 years (2004 back to 1971). Because the identification and estimation of the permanent variance, and therefore of the transitory variance as well, depends on identifying the permanent component from the long autocovariances, this could generate a difference. In addition, for the approximate nonparametric method, Moffitt and Gottschalk used lags of order 10 or higher, whereas we use lags of order 4 and higher for the LEHD approximate nonparametric method.

implied by the error components model, which are more convenient for interpretation of

magnitudes of trends in the variances than the alpha and beta parameters. This figure shows that

the total variance all of log earnings showed no significant trend between the mid-1980s and the

late 1990s. The recent rise in the total variance primarily reflects changes in the permanent

variance which started increasing in 1996. While the transitory variance fluctuates it shows no

clear trend in the recent period.

Finally, Figure 8 shows the estimates of the transitory variance obtained from the

approximate nonparametric method developed in Moffitt and Gottschalk (2008). While this

method makes much weaker assumptions than the error components model, it shows very similar

patterns. The transitory variance fluctuates with the business cycle but shows no clear trend after

the early 1980s.

Estimates for the LEHD are shown in Figures 9-11. Figure 9 shows the estimates of

alpha and beta from the parametric error components model.13 While these LEHD series are

considerably smoother than the series for the PSID shown in Figures 4 and 5, the estimated

changes in both, especially that for beta, which drives the transitory component, are similar to

those estimated for the PSID. Specifically, beta declines from 1991 to the late 1990s then rises

sharply thereafter, returning in 2003 to about the same level it had been in 1991. As discussed

above, this is qualitatively similar to the cyclical patterns shown for the PSID.

However, a major difference is in the magnitudes of the decline and fall, which are much

smaller for the LEHD than for the PSID. This probably mirrors the smaller magnitudes of

decline and rise in the overall variance noted in the discussion of Figure 2, and may arise from

the same source.

Figure 10 shows the fitted, or implied, permanent and transitory variances for the LEHD

from the error components model. Not surprisingly, these permanent and transitory variances

change less than those for the PSID. This reflects a flatter alpha and beta plots in figure 9.

Another difference is that the PSID transitory variance (see Figure 7 above) ends up in 2003

slightly below its cyclical peak in 1991 whereas it ends up in 2003 slightly above its 1991 value

in the LEHD. These differences are small, however.

Finally, Figure 11 shows the estimates of the transitory variance from the approximate

nonparametric method. The LEHD estimates are quite similar to those obtained from the

parametric error components model, as they were for the PSID as well. This confirms that our

estimates are not being driven by the parametric assumptions in our error components model.

Summary

This preliminary investigation into whether the trends in transitory variances of male

annual earnings estimated in the Panel Study of Income Dynamics are also found in an

administrative data set, the Longitudinal Employer Household Dynamics data, reveal a rough

consistency in the overlap period, 1991 to 2003. Specifically, transitory variances declined

slightly in the first half of the period and then rose for what are likely to have been cyclical

reasons, with no strong or apparent trend. However, the magnitudes of the fluctuations are much

smaller in the administrative data than in the survey data. Indeed, the total variances move

much less in the LEHD than in the PSID or a CPS sample with sample deletions similar to those

used in the LEHD. We will explore possible explanations for this difference in future work.

13 The other parameters are shown in the Appendix.

Table A1 Estimated Parameters from Error Components Model

LEHD PSID V(mu_a0) 0.310 0.090 rho 0.638 0.847 theta -0.400 -0.574 V(omega) 0.014 0.003 V(delta) 0.0001 0.0000 Cov(mu_delta) -0.009 -0.002 Gamma_0 -0.033 -0.033 Pi_0 0.329 0.063 Pi_1 -0.0003 0.0020

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Figure 1:Mean Log Male Earnings in the CPS and LEHD1990-2004

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In this and subsequent figures, the four PSID non-interview years are interpolated from the two adjacent points. Trend line is fit from a fifth-order polynomial. Source: Moffitt and Gottschalk (2008)

Figure 5: Error Components Model Estimates of Beta: PSID

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Year

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

TransitoryUnemployment Rate

Figure 7: Fitted Permanent, Transitory, and Total Variances of Male Log Annual Earnings, Age 30-39: PSID

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

Year

PermanentTransitoryTotal

Figure 8: Approximate Nonparametric Estimate of Transitory Variance: PSID

0

0.05

0.1

0.15

0.2

0.25

0.3

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

yearAveraged over all ages.

.92

.92

.92.94

.94

.94.96

.96

.96.98

.98

.981

1

11.02

1.02

1.021.04

1.04

1.041.06

1.06

1.061991

1991

19911993

1993

19931995

1995

19951997

1997

19971999

1999

19992001

2001

20012003

2003

2003year

year

yearalpha

alpha

alphabeta

beta

betaEstimates of Alpha and Beta by Year: LEHD

Estimates of Alpha and Beta by Year: LEHD

Estimates of Alpha and Beta by Year: LEHDFigure 9: Error Components Model--Figure 9: Error Components Model--

Figure 9: Error Components Model--

.25

.25

.25.3

.3

.3.35

.35

.35.4

.4

.41991

1991

19911993

1993

19931995

1995

19951997

1997

19971999

1999

19992001

2001

20012003

2003

2003year

year

yearperm

perm

permtrans

trans

trans from Error Componets Model: LEHD

from Error Componets Model: LEHD

from Error Componets Model: LEHDFigure 10: Fitted Permanent and Transitory VaraincesFigure 10: Fitted Permanent and Transitory Varainces

Figure 10: Fitted Permanent and Transitory Varainces

.25

.25

.25.3

.3

.3.35

.35

.35.4

.4

.41991

1991

19911993

1993

19931995

1995

19951997

1997

19971999

1999

19992001

2001

20012003

2003

2003year

year

year(mean) permvar

(mean) permvar

(mean) permvar(mean) transvar

(mean) transvar

(mean) transvarfrom Approximate Nonparametric Method: LEHD

from Approximate Nonparametric Method: LEHD

from Approximate Nonparametric Method: LEHDFigure 11: Permanent and Transitotry VariancesFigure 11: Permanent and Transitotry Variances

Figure 11: Permanent and Transitotry Variances